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Biodiversity Journal, 2018, 9 (2): 149–166

Is biodiversity aging? Heuristic questions on the taxonomicdiversity in the Phanerozoic

Longino Contoli Amante

Via Arno 38, 00198 Roma, Italy

ABSTRACT

Received 02.05.2018; accepted 12.06.2018; printed 30.06.2018; published online 05.07.2018

The trend of numerosity component of diversity was analysed from palaeontological data,according to various time intervals and taxonomical ranks. Taxa numerosity of lower (withrespect to family), with a nearly exponential increase, vs. higher ranks (from order to macro-taxon), with mainly a logarithmic trend, confirms to follow quite different patterns over time.This dataset seems to fit with a more assortative hypothesis, for higher taxa and a more divi-sive one for lower taxa. Then, a model was built to quantify the relative weight, over time, ofthe above hypothetical evolutionary components of various taxa ranks; such ranks were iden-tified, in a palaeontological approach, by the maximum number of recorded taxa or, in aphyletic approach, by the time duration based on genetic data. The trends obtained by thismodel agree with observed records and the hypothesis, to be verified, of a quite different evo-lutionary origin of macro- (phylum, class, order ranks) and micro-taxa (genus and species),during the transition between two main time phases: the first (evidently more assortative),mainly linked to the lateral sharing of characters, the second (evidently more divisive), mainlyinfluenced by the ever growing morpho-physio-genetic isolation even for the protection ofcomplex adaptations, as in the present, “modern species”.

INTRODUCTION

Since evolutionary theory was accepted as theonly possible rational explanation of the life diver-sification in the biosphere - e.g., Gould (2002); seealso Mayr (1982), evolutionary processes have re-ceived many and different interpretations. Twomain question points have been particularly inves-tigated: (i) the basis of the biological variability, and(ii) the factors orienting its evolution: see, e. g.,

Gould (2002). Moreover, genetics has provided ex-perimental evidence of the “transition” from aspecies into another species, within a frameworkthat has been defined “microevolution”.

However, there has been a contextual difficultyin explaining the great differences in morpho-phys-iological models, occurring among high-rank taxalike phyla, classes, and orders by means of merelymicro-evolutionary processes (Stanley, 1979).

Therefore, Stanley (1979) hypothesized a “de-coupling” of selective ranks, between microevolu-tion (selection among individuals) and macro-evolution (species as individual units of selection,in macro-evolution, in analogy with specimens inmicro-evolution).

KEY WORDS Evolutionary models; genetic timing; macroevolution; taxonomic diversity.

“Iamque adeo fracta est aetas effetaque tellus vix animalia parva creat quae cuncta creavit

saecla …” (Lucretius).

DOI: 10.31396/Biodiv.Jour.2018.9.2.149.166

tween that of orders and genera, perhaps due alsoto the variety of taxonomic approaches.

There was also a great difference among the var-ious models proposed to interpret the patterns oftaxonomic diversity in the Phanerozoic (see, e.g.,Valentine, 1970; Valentine & Moores, 1970;Schopf, 1979; Wise & Schopf, 1981; etc.). Thisgreat difference can be interpreted as a possible in-fluence of the taxonomic rank chosen by the differ-ent authors (Lane & Benton, 2003; Markov &Korotaiev, 2007), i.e. a low rank (species-genus)(Raup, 1976a, b; Bambach, 1977; Valentine et al.,1978) or at high-rank (order etc.) (Gould et al.,1977; Sepkoski, 1978). Indeed, also the “consen-sus” model (Sepkoski, 1978) showed that there wasa high numerosity of higher taxa in the most ancientphase of the history of life, and a higher numerosityof the lower taxa in the most recent phases. In par-ticular, both the low taxa numerosity during theearly phases of the history of life, and the Cenozoicexplosion of low-rank taxa, cannot be attributed toartefacts (Signor, 1978, 1982, 1985). Anyway, Ben-ton & Emerson (2007) did not consider that it ispossible to identify a single model explaining thewhole variety of contexts and taxonomic ranks. Im-portant new discoveries (such as for the “evo-devo”) have strongly challenged and re-evaluatedold certainties (Gould et al., 1977; Gould, 1989,2002). For instance, on the homologies and analo-gies of characters, the prevalent stability of evolu-tion over time with relatively strong accelerationsthrough cladogenesis, hierarchic selection models(from gene to species and beyond), evolution by re-ductive instead of addictive diversification of thegene complexes, and historical evolution of a sameaptitude-to-evolve and the role of the complexityscience in the evolutionism (Kauffman, 1993).

This fact has carried to important intuitions, al-though these intuitions have not been alwaysdemonstrated: e.g., the structural approach to theform-function relationship (i.e., exaptation) or a dis-tinct “historic” determinism of the macroevolution,partly differing from that of microevolution (Gould,2002).

So, it has also been proposed to place, togetherwith the classical view of an adaptive evolutionthrough qualitative mutations, also an evolutionthrough progressive complexification due to the in-creasing of the hereditary pool (Ohno, 1970; Bate-son, 1979; Taylor, 1979; Omodeo, 1985, 2010). In

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Hence, in order to explain the sudden appear-ance of organization plans totally innovative, evo-lutionary biologists invoked mechanisms - seeGould (2002) for an extensive synthesis, that in-clude exaptation, polyploidization, neoteny, lateraltransmission, and the passages from individual tocolony (or society) to super-individual, related topatterns of complexification of genic complexes, upto the confluence of morphophysiological charac-ters of different taxa in a single one through, e. g.,endosymbiosis, parasitism, trophism, hybridizationeven between well distinct groups, up to the con-fluence of various taxa into a single biological cycle(Landman, 1991; Doolittle, 1998, 2000; Goldenfeld& Woese, 2007; Gould et al., 2008; Sanchez–Puerta& Delwiche, 2008; Archibald, 2009; Dagan & Mar-tin, 2009; Kleine et al., 2009; Rogozin et al., 2009;Liu, 2011); see also Williamson (2003); recently,Oakley (2017), with a formal and general approach.

It remains, however, to be discussed whether thecomplexification of the above-mentioned mecha-nisms is just a sub-group of the whole complexifi-cation, which includes also the dimensionalincrement, coloniality, sociality, and even the indi-rect development (with or without metamorphosis).

In addition, it has been observed that the geneticroots of micro- and macro-evolutionary aspects maybe surprisingly coincident (Gompel et al., 2005).

According to a classical view: e.g., Rensch(1959), the emerging of new, increasingly differen-tiated taxa into the history of the life on earth,should have been gradual in time (i.e. from speciesto genus, from genus to family, from family toorder, etc). However, since the Palaeozoic, there hasbeen a tumultuous appearance of the majority of thegreater taxa, whereas in more recent times there hasbeen a huge increment in the appearance of thenumber of minor taxa such as species and genera(Signor, 1978, 1982, 1985; Raup, 1983; Benton,1993, 2001; Smith, 2001; Sepkoski, 2002; Lane &Benton, 2003; Bush & Bambach, 2004; Jackson &Johnson, 2001; Holland & Sclafani, 2015; but see,e.g., Mc Gowan & Smith, 2008; Ruban, 2010).Nearly all these minor taxa can, however, be in-serted into already-known greater taxa (orders,classes, and phyla).

The family rank, appears to be intermediate andpivotal even in relation to the previous topic and therelevant trend (Sepkoski, 1979; Benton, 2001; Ben-ton & Emerson, 2007) appears as intermediate be-

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the present paper, the expression “assortative evo-lution” was preferred, as evolutionary complexifi-cation linked to the confluence of distinct anddifferent taxonomic sources.

Palaeontology is ever fundamental to under-stand the distribution and evolution of biologicaltaxa during the history of the Earth and to definethe time intervals characterizing the main phases ofevolution. Today, such studies are positively sup-ported by neontological advances, e. g., of geneticsand its molecular bases. In any case, there is now awide consensus, e.g., in determining as the begin-ning of the Phanerozoic the formation of a “mod-ern” atmosphere, conditioned by O2, around 600Ma (Farquhar, 2009; Omodeo, 2010; Karhu, 2012).Possibly, in time, the biosphere, which was nearlyvirtual in the early phases, assumed a real volumebecoming with time more and more influenced,even in its abiotic components, by living organismswhich were increasingly conditioned in their mor-phological evolution by bio-coenotic interactionsand the relative adaptive responses (Butterfield,2007).

Hence, if the early interactions occurred mainlywith the abiotic environment (i.e. they could be fun-damentally biochemical interactions), the successiveinteractions were mainly done with the biotic envi-ronment, through ecological niche processes such ascompetition, predation, and mediating characteristicssuch as vagility, modularity, body size increases, etc.Hence, with the Phanerozoic, it became possible thereliable identification of the greater phyletic groupsbased on macro-morphology of taxa.

Indeed, until now the determinism of the earlyphyletic diversification versus the later diversifica-tion of the lower taxa remain extremely doubtful.

A suite of analyses was applied to these morpho-logically identified taxonomic groups, in order totest whether the numerosity pattern over time of thehigh-rank taxa (phyla, classes, orders; see, e. g.,Contoli & Pignatti (2011) and of the low-rank taxa(genus, species) may have a substantially differentcausal origin; so perhaps extending the ideas ofWoese (2002; 2004) up to the last part of the pre-Cambrian.

In particular, it has been verified:

whether and how much the trends of numerosityof more or less inclusive taxonomic ranks (e. g.: or-ders v.s genera) differ from each other over time;

what are the implications, about these trends, ofthe theoretical assortative or divisive outlines;

if these patterns prevail in the outlines observedin real taxonomic ranks;

the predictivity of a model based only on theabove mentioned theoretical outlines, in relation tothe relative numerosity of taxonomic ranks accord-ing to the fossil record.

MATERIAL AND METHODS

Sources of data

To analyze the curve fitting of observed nu-merosity of orders and genera over time, the datareported have been used, even in a graphic way, byBenton (2001).

The macrotaxa (see above in the text) and orderswere considered “large taxa”, “small taxa” the gen-era and species. If one compares between them arank of a small taxa with one of the large taxa with-out emphasizing most of the differences, among thepossible comparisons in the hierarchical successionof ranks, orders and genera are the least distant and,therefore, their comparison is the most prudent.

Chronology

To evaluate the temporal patterns of the record,considering also the observations of Benson &Mannion (2011) and Lloyd (2011), the time valuesof the geological periods were not used directly; in-deed, in order to estimate the numerosity of taxa,the time of passage from increasing and decreasingtrends or vice versa has been used, i. e., the maximaand minima peaks separating following trends.

When it was convenient, the record was subdi-vided into intervals of 100 million years, utilizingthe highest number of taxa observed, independentlyfrom conventional boundaries of geological peri-ods, in order to buffer the more or less random en-vironmental fluctuations on which the aboveboundaries are usually based.

Indeed, considering the maximum values foreach period means taking into account the real po-tential for each period, thus avoiding all those con-tingences which may have conditionedstochastically the duration and the strength of theobserved “minima” or of the “extinction crises”.

Is biodiversity aging? Heuristic questions on the taxonomic diversity in the Phanerozoic 151

For numerosity frequencies relative to familiesthe values suggested by Raup (1976a, b) and fol-lowed by Signor (1978, 1982, 1985), Benton(2001), Jackson & Johnson (2001), Sepkoski(2002), Benton & Emerson, 2007), Smith (2007)and Contoli & Pignatti (2011), were compared.

Methodological problems about Taxonomy

The most complete dataset in terms of both con-tinuity and regularity regards marine animals.

Owing to the obviously very different samplingcompleteness of neontologic vs. palaeontologicsampling, only the latter data were used, even incase of the Cenozoic.

It is also obvious that the same taxa ranks in dif-ferent phyla may not be always perfectly equiva-lent; however, they are equivalent in terms of theirrelative inclusiveness and morphological differen-tiation relatively to the other ranks. Even the evo-lutionary similarity inferred by time duration databased on genetic distance (see Appendix 1 and 2,online) shows that the mean duration of taxa foreach taxonomic rank should be different and distin-guishable, even if partially overlapping.

So, in the model, instead of the absolute ones, ithas been preferred to use frequencies, relatives tothat of families, as a pivotal taxonomic rank.

To test, with the model, the hypothesis that thetrends over time of different taxonomic ranks de-pend on their relative numerosity with respect to theintermediate one of the families, values from liter-ature were needed, even if approximate.

Analysing the whole palaeontological record,Sepkoski (2002) seems to suggest that there is one-order of magnitude difference among the numerosi-ties of successive taxonomic ranks.

Other authors (Jackson & Johnson, 2001) con-sider that the ratio between coexisting genera andspecies should be between 1 to 10 and 1 to 5.

Benton (2001) inferred a ratio of 1 to 4 betweenfamilies and genera or of 5 to 1 between familiesand orders.

Moreover, according to Smith (2007; Fig. 7), theaverage ratio between species and families is ≈64;so, it was inferred, between genera and families, theaverage ratio of 8 to 1 ≈√64.

Lastly, the ratio of ≈0.034 between macrotaxaand families is implicitly suggested by Contoli &Pignatti (2011).

Analogically, between orders and families, itwas inferred the average ratio of 1 to 5 ≈√0.034.

Therefore, according to the above mentionedAuthors, the minimum and maximum frequencies,related to families, were, for macrotaxa, respec-tively ≈0.01 and ≈0.035 (rounded up to 0.04); fororders ≈ 0.1 and ≈0.2; for genera ≈4 and ≈10; forspecies ≈20 and ≈100.

It is clear that, for this last rank, a homogeneousconcept of species would be needed, for the studyof the origin and end of the same, taking also intoaccount, the appropriate observations of Ezard et al.(2011).

Then, the model was tested with the above 2 se-ries of relative frequencies.

Biodiversity

To be emphasized, the present work was notlooking for a richness analysis, but for a numerosityone, thus not linked to any weighting procedure.

On the other hand, numerosity can be consid-ered, not only as a weighting base (e.g., for richnessevaluation; see also Ganis, 1991; Contoli Amante,2007, Contoli Amante & Luiselli, 2015), but also initself, especially if pertaining to the same scale ofdata source.

In order to make a proper taxonomic numerosityanalysis at the biospheric scale, it is necessary toapply an approach not influenced by evenness.

So, the unweighted taxa numerosity data fromliterature was directly used.

The model

To propose an explicative model of differenttrends observed in various taxa ranks, it was neededto parameterize their characters. Note that, if the bi-ological meaning of the various taxa ranks isstrongly subjective, nevertheless the above ranks,by definition, represent a hierarchic series of taxo-nomic ranks (subdividing the same set of organis-mic individuals) from the less to the morecomprehensive and, so, including, among their in-dividuals, respectively a greater or a lesser “evolu-tionary similarity”.

Obviously, in a given lineage, a taxonomic rankis more comprehensive, while its numerosity is less,i. e. the numerosity of the taxa of the same rank;and vice versa.

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So, for each taxonomic rank, the average evolu-tionary affinity between the various taxa can be ex-pressed by the numerosity of the given taxonomicalrank. Indeed, since the main taxonomic ranks areformally the same, across the whole life in the earth,every taxonomic rank includes and subdivides thewhole fossil record and its diversification range; so,if that range is subdivided on more v.s fewer singletaxa of a given rank, each of the above, single taxamust be, conversely, fewer v.s more different in itsevolution; it results that higher numerosity at agiven rank corresponds to higher average evolution-ary similarity in a given taxon of the same rank.

The work was interested to compare betweentaxonomic ranks, not their absolute values; thus, therelative numerosity, with respect to families, of taxaof each rank will be the searched parameter of themodeling analysis.

The model can be applied to any temporal scalestarting with the Phanerozoic and ending with thepresent.

Palaeontology

The maximum recorded number of taxa pertain-ing to the “i” rank can help to parametrize the var-ious ranks. Moreover, the taxa numerosity of “i”should be directly proportional to an “evolutionarysimilarity” within such a taxon rank.

In the hypothesis to be modelled, in a first phase(assortative and logarithmic), the evolutionary di-vergence was mainly expressed by more compre-hensive and, so, less rich taxa ranks; in a followingphase (divisive and exponential), by less compre-hensive and richer taxa.

In the “taxa in time” model, a logarithmic andan exponential component inversely linked to max-imum number of taxa were summed, among therecorded time periods of the Phanerozoic.

By dividing the “i” numbers of taxa (pertainingto the taxonomic ranks of macrotaxa, orders, fami-lies, genera, and species) by that of families, as anintermediate taxonomic rank, it has been obtained:

N° taxa “i” originated at “t” time = = k [log (t/t “final” x taxa “families”/taxa “i”) ++ exp (t/t “final” x taxa “i”/taxa “families” )].

Genetic data

Methods were, since long time, conceived andrefined, even when with not ever converging results,

to evaluate the splitting time among taxa, estimatingso also their duration. Altogether, clear differencescan be observed among the various taxonomicalranks: in general, the more the duration of a taxo-nomic rank, the more it was comprehensive.

Their average duration in geological time can bea way to parameterize them and, conversely, to es-timate their “evolutionary similarity”, for the pur-pose of this present work, even while being awareof the partial uncertainty of these estimates (cfr. e.g. Warnock et al., 2011; Duchène et al., 2017).

In this perspective, from various sources (No-vacek, 1992; Michaux et al., 2001; Dubey & Shine,2010; Hedges & Kumar, 2009; Murphy et al.,2012), it has been inferred time duration of a lot oftaxa examined by the above Authors and pertainingto the above 5 ranks; then, an estimation of mini-mal, maximal, and average duration of each taxo-nomic rank was obtained.

In order to prevent that the average mean of “i”could be influenced too much by:

- the numbers of richer or poorer taxa;- the maxima or minima, perhaps mainly subject toerrors as outliers, were excluded, from utilized data,the extreme maxima and minima;- were averaged the minus- and plus-variant data ofthe same level (i. e., first and last, second and penul-timate, third and last-but-two, etc.), up to meansregularly invariant in the first significant numbers.

As for palaeontological data, for genetic ones itwas obtained:

N° taxa “i” originated at “t” time == k [log (t / t “final” x duration of taxa “i”/durationof “families”) ++ exp (t / t “final” x duration of “families”/durationof taxa ”i”)].

Relationships between palaeontological andgenetic data

As yet suggested, evolutionary similarity of “i”can be conceived as directly proportional to themaximum taxa numerosity and inversely to its timeduration; so, between taxa numerosity and time du-ration an inverse relation was expected and ob-served.

Extinction

From the number of taxa of “i” rank and from


their durations, considering the extinction inverselyproportional to minimum duration reported to theaverage one, the extinction rate was estimated:N° taxa “i” extinct at “t” time = 2 x t/t “final” timex taxa “i” at “t” time/(minimum duration of “i”/mean duration of “i”).

An algorithm proposed for the model:

N° of “i” taxa present at “t” time = N° of “i” taxaoriginated in “t” time - N° of “i” taxa extinct in “t”time.

i. e.,

N° of “i” taxa presents at “t” time == k {log [(t time / t “final” time)/mean evolutionarysimilarity of taxa “i” + 1] + exp (t time/ “final” timex mean evolutionary similarity of “i” taxa) -- 2 x t time/ “final” time x “i” taxa originated at “t”time/(minimum duration of “i”/mean duration of“i”)]}.

Fitting of the data

To fit the data from literature with a suitablepolynomial, was searched for functions of thesmaller degree compatible with a substantially max-imal significance; so, all polynomials of growingdegree (1, 2, 3…) were calculated and then the R2values were regressed vs. the growing degree of thepolynomials; when the plateau was attained, thepolynomial of the corresponding degree wasadopted (see, e. g., Figs. 4, 6).

RESULTS

Theoretical advantages and disadvantages ofassortative phyla versus time and evolution

Increases in complexity are linked to the evolu-tion, with number of adaptations increasing in rela-tion to increasing physiological functions, bodysizes, and lifespan.

Hence, an eventual lateral confluence of genesand their morphophysiological expression of char-acters through their genic basis may originate a newtaxon, but this may be true only if the joininggenomes are compatible for some essential preex-isting adaptations. In the extreme hypothesis of asingle new adaptation to be conserved, there will be

a 75% of useful assortments (i.e., with at least one+ for each character) (Table 1), whereas in the caseof two adaptations, the vital crosses will be approx-imately 56% (Table 2), and so on. For the case ofone new character added to a previous set, see fig-ures 1, 2.

So, there should be a logarithmic decrease in theevolutionary prospective of the potential intertaxahybrids during the evolutionary complexification.

Moreover, the adaptive advantage of a hybridtaxon should depend also on the available nichespace, which tends to diminish with time due to theincreasing competition strength, thus compensatingad abundantiam the free niche space after cata-strophic events. For both reasons, during the evo-lutionary complexification there must be areduction of the assortative evolution opportunities.

Recorded numerosity of taxa through time

The recorded variations in the number of lowertaxa (genera) and higher taxa (orders) over time arepresented in figures 3, 5.

In general, a trinomial pattern was observed,with two inflexions of importance variable fromrank to rank. The two curves were very different:the initial portions of the two curves were signifi-


Table 1. Viability of potential assortments of 1 character for each taxon.

Table 2. Viability of potential assortments of 2 characters for each taxon.

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Figure 1. Theoretical compatibility of an added character to a previous set. Figure 2. Compatible assortments of an addedcharacter vs. the previous set. Figures 3, 4. Variation in the number of lower taxa (= genera) over time (Fig. 3) ; the degreeof the polynomial corresponds to the flex of the “P^/degree” curve (Fig. 4). Data reported by Benton (2001). Figures 5, 6.Variation in the number of higher taxa (= orders) over time (Fig. 5); the degree of the polynomial corresponds to the flex ofthe “P^/degree” curve (Fig. 6). Data reported by Benton (2001).

155Is biodiversity aging? Heuristic questions on the taxonomic diversity in the Phanerozoic

cantly positively correlated (P < 0.05; one-way AN-COVA), whereas there was no correlation as for thefinal portions of the curves (one-way ANCOVA; P>0.25).

If the significantly fitted polynomials were to beconsidered, the derivate is negative in the earlyphases and positive in the late phases. The firstphases tend to prevail in the generation of the highertaxonomic categories, and the late phases in thegeneration of the lower categories, which tend tohegemonize the taxonomic numerosity with timeelapsing.

Does time theoretically explain the passagefrom micro- to macro-evolution?

The theoretical relationships between time andnumber of taxa, for both lower taxa (species) andhigher taxa (orders) (see Table 3 for the raw data),in the hypothesis of a constant time interval passingbetween each hierarchic passage from a given tax-onomic category to another, are presented in figures7, 8. It should be noted that the patterns seems con-sistent with the real data in the case of species, butnot as for the macro-taxa, as this hypothetic latterpattern was even more exponential than that relativeto species. Hence, in this case, the time cannot sim-ply explain the observed patterns and, namely, thehypothesis of an “autocatalytic” increase in time ofthe more comprehensive taxa is untenable.

Modeling analysis

Genetic data are summarized in Table 4. Avail-able palaeontological (Max n.r of observed taxa)and genetic (Minimum, average, Maximum dura-tion in time) data suggest (Table 5) the relevant val-ues of evolutionary relatedness among taxa of thesame rank, relatively to the families.

In both kind of data, the model (Figs. 9–21; P:palaeontology; G: genetics) shows a trend from amore logarithmic pattern (macrotaxa and orders) toan exponential one (genera and species).

Because the model is relativized to families, val-ues and graphs of such taxa express only the timeand cannot account for any fluctuation.

The analysis of Correspondence (detrended ornot), Principal components, and Clusters (accordingto Ward, Euclidean Distance and Single Linkage)shows the central position of time and two distinctgroups of variables (both from the record and the

model), representing, the first the smaller taxaranks, the second the larger ones, well separated bythe first axis representing the very bulk of variance(Figs. 22, 23); the recorded families seem to joinbetter the smaller taxa, near to the recorded genera;nevertheless, the best fit for families (Fig. 24) iswith a first degree (straight) function of time, morethan a logarithmic (prevailing at first) or an expo-nential one (prevailing at the end), in agreementwith its intermediate and pivotal position among thetaxonomic ranks, confirming Hoffman (1985).

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Table 5. Ratio between number of taxa at a given taxonomicrank and number of taxa at family rank, as estimator of theevolutionary relatedness.

Table 4. Genetic duration (10^6 years).

Table 3. Hypothetical hierarchical increases of various ta-xonomical ranks in time, according to the gradualist hypo-thesis.


Figures 7, 8. Relationships between time and number of taxa, for both lower taxa (species: A) and higher taxa (macrotaxa:B), in the gradualist hypothesis of a constant time interval passing between each hierarchic passage from a given taxonomiccategory to another (see Table 3). Fig. 7: species (ordinatae) v.s time (abscyssae). Fig. 8: macrotaxa (ordinatae) v.s time(abscyssae).

157Is biodiversity aging? Heuristic questions on the taxonomic diversity in the Phanerozoic

Among each of the above two very separated setof variables, the proximity between recorded andmodel ones of the same rank is less evident, perhapsdue to the role of stochastic paleo-geologic events,clearly not affecting the model.

DISCUSSION

Synthesising the main results

In general, the patterns about the taxa numeros-ity which have been highlighted in previous studies(at least since Signor (1985) until Foote (2010)were confirmed, although there were some differ-ences which were mainly due to different authors’perspectives.

The approach developed by Alroy (2008) andAlroy et al. (2010) was not used in the presentstudy. Indeed, although this approach (anyway, stillin progress; see Marshall, 2010) is of great rele-vance for the standardization and comparison of thecoenotic data under an ecosystemic key, it may sac-rifice a conspicuous part of the available samplesthat are instead essential for the present study. Inaddition, the above-mentioned approach obviouslyenhances the contingent short-term oscillations anddepresses the long-term oscillations, that are insteadcrucial for the scopes of this paper.

In short, the above approach is mainly devotedto richness component of biodiversity, when thepresent one concern essentially the numerosity.

Hence, the two approaches are not antagonist,but are simply linked to different components ofbiodiversity and different spatio-temporal scales.

This may partly explain the hyperbolic trendfound by Markov & Korotayev (2007) andDmitriev (2011). However, the general pattern andthe determinism of such aproaches do not contrastwith the present analysis. Thus, given the above-mentioned approaches, so different in the estima-tion of changes in palaeontological biodiversity, itwas not considered to be appropriate to modify, ina hyperbolic key, the exponential trend deduced,e.g., by Sepkoski (1967, 1979, 2002) and (Benton,2001).

Notwithstanding the great methodological dif-ferences, the results of the two approaches on thetaxonomical diversity in the Phanerozoic (see Sep-koski, 1967, 1979, 2002; Benton, 2001, followed inthis work about numerosity) compared to Alroy,(2008), or Foote (2010), concerning richness, arenot irreconcilable (see, e.g., Foote, 2010: fig. 18.6)and do mirror in highlighting two distinct growthphases: a first, apparently self-limiting phase, anda second, nearly autocatalytic phase, with a long“crisis” separation. These results are hence in har-mony with the findings of this work, highlighting


Figures 9–11. Macrotaxa; model P1 (Fig. 9), P2 (palaeontology) (Fig. 10), and G (genetics) (Fig. 11) v.s relative time (0-700 x 10^6 years). P; m/f = hypothesized numerosity ratio “macrotaxa/families”. Figures 12–14. Orders ; model P1 (Fig.12), P2 (palaeontology) (Fig. 13) and G (genetics) (Fig. 14) v.s relative time (0-700 x 10^6 years). P; o/f = hypothesizednumerosity ratio “orders/families”.

non-obvious differences between macro- andmicro-taxa.

Indeed, with time (i) a mainly logarithmic in-crement followed by a constancy in the number ofmacro-taxa (i.e., maintenance of phyla and part ofthe classes with orders being frequently substi-tuted), and (ii) a nearly exponential growth in thenumber of micro-taxa were observed.

In the above perspective, the intermediate fam-ily rank appears to be a quite heterogeneous andperhaps composite one.

Hence, the present results showed an emerging,and not at all merely formal, difference between

macro- and micro-taxa as well as between macro-and micro-evolution (Gould, 2002). Indeed, thetemporal pattern of the macro-taxa is consistentwith a self-limiting model, whereas that for themicro-taxa is typically self-enhancing.

Whilst the micro-taxa patterns (from species tofamilies) are consistent with expectations of thegradualist theory (evolution is essentially a functionof time), since at least the Permo-Triassic crisis, themacro-taxa are remarkably different from such ex-pectations, but in agreement with the assortative hy-pothesis and not in contrast with Gould (2002) andEldredge (2015).

Is biodiversity aging? Heuristic questions on the taxonomic diversity in the Phanerozoic

Figure 15. Families; model P (palaeontology) and G (genetics) v.s relative time (0-700 x 10^6 years). Figures 16–18. Genera;model P1 (Fig. 16), P2 (palaeontology) (Fig. 17) and G (genetics) (Fig. 18) v.s relative time (0-700 x 10^6 years). P; g/f =hypothesized numerosity ratio “genera/families”.

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To finish, it was observed a clear similarity be-tween the theoretical and the observed patterns intime for macro-taxa (Fig. 2 vs. Fig. 5) contrastingwith micro-taxa (Fig. 7 vs. Fig. 3), according to twovery different hypotheses.

These results encouraged to suggest a quite sim-ple model which, according to the above hypothe-sis, can unambiguously explain the biological basisof temporal patterns of relative numerosity of bothmacro- and micro-taxa, considering also the chosentime scale (10^8 years) which smooths the effect ofextinction crisis.

Due to its coarseness, the model shows onlyschematically the relative numerosity basal trendsover time of the various taxonomic ranks, with re-spect to families.

The scope of the model was not to reflect thefluctuations, perhaps mainly stochastic, linked tothe crises of numerosity, particularly during thephases of the “large extinctions”, especially evidentat family rank; on the other hand, there is a short-coming in the model: it, by definition, cannot showthe variation in the growing rate of the families,considered as stable over time.

Nevertheless, the model seems to be quite ro-bust: the obtained trends show very few variationseven if the analysed values of the taxonomic ranksdo vary around an o. o. m. (order of magnitude).

The model, when applied to palaeontological orgenetical data, shows quite similar results even vs.the observed patterns of the bulk of two maingroups of various modellized taxonomic ranks(macrotaxa and orders v.s genera and species) overtime.

It seems that the hypothetic prevalence of the as-sortative or the divisive evolutionary mechanismcan be sufficient to explain (even if not at all toprove!) the differing basal trends in time of thelarger v.s smaller taxonomic ranks.

Finally in the model, the start of Phanerozoic(“0” time in the analysis and “1+0” in some graphs,for computing purposes) seems to be analogue, forlarge taxa, to a “veil line”, hiding a previous phaseof great phyletic diversification.

Is the sampling reliable or is it mere artefact?

An important objection to the palaeontologicalrecord analyses is linked to the theoretically pre-dictable pattern of the curves “groups/individuals”.


Figures 19–21. Species; model P1 (Fig. 19), P2 (palaeonto-logy) (Fig. 20) and G (genetics) (Fig. 21) v.s relative time(0-700 x 10^6 years). P; s/f = hypothesized numerosity ratio“species/families”.

These curves would predict, for the groups, a nearlylogarithmic growth up to an upper limit (the real nu-merosity) positively related to the sample size in-creases. Indeed, it would be expectable that thesample sizes increase regularly and significantlywith time from the geological ages to the present.

This eventual bias would at best explain in partthe earliest phase of the macro-taxa curve with time,but certainly not the final phase.

Moreover, the rapid exponential growth of thefinal phase of the micro-taxa curve (sometime, eventowards a kind of saturation of a real ecosystemspace; see Machac et al., 2013) is clearly against theabove-mentioned predictions, which would be nec-essarily linked to functions of logarithmic (and notexponential) type.

In general, the high fit of the trends over timewith a third degree positive polynomial modelseems to be quite different to the logistic one, the-oretically expected in such a context.

In addition, it does not seem that the importanceand completeness of the palaeontological samplingincreased with time in the above-mentioned way(Signor, 1985). On the contrary, there are remark-able oscillations and unpredictable decreases evenin recent periods because some taxa are unlikely tofossilize especially under some environmental con-ditions (Signor, 1985; Gould, 2002).

Thus, the observed patterns cannot be explainedby classical “groups/individuals” models.

Did the observed patterns derive from theevolutive interaction between inter-taxa as-sortative potentiality and, conversely, subse-quent isolation needs for adaptations toreproductive isolation?

Assortative evolution is often considered as ex-ceptionally rare in the present time (however, seeGontier, 2015, without neglecting the hypothesis asbrilliant as extreme, between the metaphorical andthe paradigmatic, by McInerney et al., 2011) and,possibly, long before the starting of the Phanerozoic(Gould, 2002).

Some doubts about its frequency of occurrencein past times are still not solved, however, some in-dications have been collected. These can be sum-marized as follows:

(1) the number of known cases is regularly in-creasing (Bohm et al., 1997; Chalfie, 1998; Tyler et

al., 2006; Gould et al., 2008; Archibald, 2009;Moustafa et al., 2009);

(2) in various taxa, there is still a permanenceof karyotypes with high N despite a diffused ten-dency to Robertsonian fusions (see Wurster &Benirschke, 1967; Morescalchi, 1970; Capanna,1975);

(3) the occurrence of cases of genetic homolo-gies of structures in very distant clades; thesecases are difficult to explain under purely clado-genetic or anagenetic keys of interpretation(Gould, 2002);

(4) the likely prevalence into the genome evo-lution of an increasing diversification rather than areductive diversification (Omodeo, 2010).

There have also been some indications of thelikely gradual and increasing role played by theinter-taxa isolation over time:

(i) the multiplicity of meiosis models, evenwithin single macro-taxa, suggests that a long time


Figure 22. Detrended Correspondence analysis (B, C, andD are overprinted). A: Time; B: species (model P; 20); C:species (model P; 100); D: species (model G; ); E: species(observed); F: genera (model P; 4); G: genera (model P; 10);H: genera (model G); I: genera (observed); J: families (ob-served); K: orders (model P; 0,2); L: orders (model P; 0,1);M: orders (G); N: orders (observed); O: macrotaxa (modelP; 0,04); P: macrotaxa (model P; 0,01); Q: macrotaxa (G);R: macrotaxa (observed). Axis 1 = 87 % of total.

161

distance has passed between the emergence of theclades and the fulfilment of each model;

(ii) the great number of inter-taxa reproductiveisolation mechanisms, which appeared well afterthe separation of many large clades;

(iii) the apparently increasing, during the evolu-tion time, of the organic (tegument, digestive - see,e. g., Doolittle, 1998 - immunitary, etc.) barriersagainst infections, parasitosis, etc.

The general hypothetical scenario: a work-ing hypothesis

Woese (2002, 2004) suggests phases of geneticsharing among organisms, before the splitting of themajor evolutionary clades, as Bacteria v.s Archaeaand Archaea v.s Eucaria, in connection with some“Darwinian thresholds” (i.e., the time limit after

which the “modern” or “Darwinian” species doarise); their increase should be linked to divisive(reproductive isolation, competition etc.) factors.

The present analyses support such hypothesisand suggest that the following macroscopic effectsof such an assortative phase may justify the trendof larger taxa, up to the early Phanerozoic. Accord-ing to the model, a kind of “Darwinian threshold”can be connected with the ever growing overcome,in o. o. m. [orders of magnitude], of the speciesnumber over that of older clades.

It is likely that the earliest biocoenotic systemswere regulated essentially by biochemical andmacro-molecular relationships rather than by mor-phological relationships, as it has surely started tooccur in later phases (Gould, 2002; Omodeo, 2010).Hence, based also on the patterns presented in thisstudy (including the sense of “veil line” suggested,in the model, by the Proterozoic-Phanerozoicboundary), it seems possible to confirm that theroots of the Cambrian explosion should be retro-dated by far, as the identification of the Cambrianexplosion by palaeontological records is inevitablylinked to the observation of macro-morphologicaldifferences among taxa.

Even genetic data seem in agreement with theabove hypothesis: according to figure 2 in Hedgesand Kumar (2009), up to about 600 Ma BP esti-mated genetic divergence did anticipate by hun-dreds of million of years the palaeontologicalphenetic one; by this period, both divergences tendgradually to synchronize.

It seems that genetic divergence, in a first (as-sortative?) phase had preceded and prepared theemerging of more advanced metabionts with com-plex development (sensu Gould, 2002).

In a second phase, due to the ever growing com-plexification of adaptations and decreasing proba-bility of an evolutionary advantage of theirassortments, possibly the isolation systems amongnew taxa have become more and more suitable anduseful, perhaps also due to a growing “evo-devo”rigidity (Valentine, 1995, 2004; Erwin, 2007).

In this phase, the bulk of genetic divergencecould became subsequent to the above phenome-non.

Thus, it is possible that, once overpassed the al-most generalized metaclade phase among the earlyorganisms (Penny & Poole, 1999; Gogarten, 2000;Woese, 2004), the potential conditions for the in-


Figure 23. Cluster analysis (Ward). A to R: see above. Figure24. Recorded Families relative to Max, in time (data fromBenton, 2001).

162

creases in richness of living organisms may havestarted in a more gradual way and perhaps even be-fore the more evident Phanerozoic explosion.

In the hypothesis of a more ancient and contin-uous presence of “phanerobionts” in the seas, andin an early phase with environmental niches not yetsaturated, there was a prevalence in the living or-ganisms of the assortative evolution innovations,with the origin of nearly all the phyla and of a greatpart of the classes, in a more biocoenotic than“chemical” context (see Penny & Poole, 1999).

The potentials for the assortative evolution in-novations tended to decrease with time in relationto a decreasing probability of qualitatively newcombinations.

Later on, in the evolution time, the various adap-tations tended to be increasingly refined and special-ized, with the risk of altering these delicate andspecialized adaptations via assortative evolution be-came higher than the potential advantages.

Hence, the inter-taxa isolation mechanisms (es-pecially, but not only, the reproductive ones) be-came prevalent, and the evolution-by-divisionreached the highest impact on the taxonomic diver-sification of the biosphere.

Overall, also in light of Woese (2002) results,the present working hypothesis is that there wouldhave been a passage from a phase with global op-portunities of structural and metabolic innovationsand of their successful genetic combinations (i.e.,expressed by the Precambrian and Cambrian explo-sions) to a phase with prevalent and increasinglyrigorous safeguard of the existing adaptationsagainst re-merging which would have been danger-ous.

As an expression of a more general pattern con-sistent with the above-mentioned scenario, there hasbeen also a tendency toward the continuous incre-ment of the relative importance of the DNA controlfraction during the evolutionary complexification(Abrahamson et al., 1973; Omodeo 2010).

Obviously, the trend described above was likelyaccelerated when the global environmental crises(such as the Permian-Triassic one) reduced substan-tially the numerosity of living taxa, thus creatingempty niche spaces for the “new species”, whichexhibited the stronger and more stable adaptations.It is from these species that the evolution wouldhave re-started, using different modes.

The increasing inter-taxa isolation was also

probably enhanced by the new requirements linkedto the conquest of terrestrial environment, includ-ing, e.g., the internal fecundation requirement, thetrophic niche diversification, etc. So, even the newcolonization of the seas by taxa returning from thefreshwater or the terrestrial environment may havealso performed some non-secondary role.

Thus, in conclusion, even towards the end of theProterozoic, the evolutionary history would havehad an early “more cooperative” phase (modulatedby inter-taxa innovations through macro-innovationand invasion of new empty niche spaces) and, also,for example, through the Mesozoic “taxa-grinder”,a successive phase dominated by competition, withmicro-differentiation and safeguard of adaptationsand already-conquered niche spaces (modulated byintra-taxa innovations), this latter agreeing with theclassical Darwinian theories.

In theory, there should be an obvious, inverserelationship between the taxonomically-basedwidth of the meta-clades and their number on thebasis of their respective hierarchic rank.

Also, in the physical sciences, it has been ob-served that the width of the free spaces covered byuseful innovations necessarily decreases with timepassing (Kauffman, 1993).

Whereas the present scenario of palaeontologi-cal differentiation does not conflict with generalphysical principles, nonetheless, it does not want toexplain the stochastic, oscillating patterns of the dif-ferent taxa during the different evolutionary times.The results, however, seem to be in part consistentwith both the classical “Neo-Darwinism” and withthe “Punctuated Equilibria” theories; less, with astrictly gradualist interpretation of the relationshipsamong taxonomic ranks, especially during the earlyphases of evolution.

In synthesis, the scenario of the work suggeststhe possibility that the taxonomic biodiversity tendsto shift increasingly and inescapably towards leastcomprehensive and more isolated taxa, i.e. frommetaclades to the modern species (Woese, 2002).If confirmed by future results, this process may behardly reversible, at least for the evolution ofmetabionts.

ACKNOWLEDGEMENTS

Tanks are due to P. Omodeo (Pisa, Italy) for the in-


sightful observations, L. Luiselli (Roma, Italy), T.Kotsakis (Roma, Italy), A. Pavesi (Roma, Italy) andmany others colleagues for the friendly assistance,J. Pignatti (Roma, Italy) for the competent consult-ing and G. Amori (Roma, Italy), R. Castiglia(Roma, Italy), F. Cruciani (Roma, Italy), for thehelpful suggestions.

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